Before the end of the day there remains 4/5 of what has elapsed since the day began.What time is it?

To best answer question, a graph can be made to show what you are saying.
beg.of day |---------------1---------------|------------2------------| end of day
where 1 represents the part of the day that has elapsed (x), and 2 represents the rest of the day (which is 4/5x).
Now we can quantify x to see how many hours it represents used the equation
(x + 4/5x) = 24 , which when solved tells us that x = 13.333... This means that 13 hours and 20 minutes have elapsed since the beginning of the day, meaning that the time is now 1:20.